Illustration of the force balancing in calculating the optical flow. The estimated corresponding position is where the internal and external forces reach the balance.
The flowchart of the proposed method.
The simulation of ultrasonic images. (a) The echogenicity model, (b) the motion field, (c) the synthetic ultrasonic image of the first frame, (d) the synthetic ultrasonic image of the second frame.
The synthetic motion fields. (a) An illustration of the motion field division. (b)–(f) Motion fields used to mimic cases where large-volume negative flow (reflux), large-volume positive flow, conflicting flow, opposite flow, and small-volume negative flow exists, respectively.
Angular error results of (a) the proposed method, (b) Molnár's method, (c) Black's method, (d) Classic+NL in a synthetic ultrasonic image pair.
Qualitative comparison in a real ultrasonic image pair. (a) Anatomy structural image, (b) color scale map, the motion magnitude and angle are encoded by saturation and hue respectively. (e) to (f) the motion fields of the proposed method, Molnár's method, Black's method, Classic+NL, respectively.
Motion vectors of (a) the proposed method, (b) Molnár's method, (c) Black's method, (d) Classic+NL in the rectangle marked in Fig. 6(a) .
Flow direction judgments of the automatic methods (cross) and visual observation (circle). 1 means positive flow, −1 means negative flow, and 0 means no conclusion is drawn.
The evaluation of the compared methods in synthetic ultrasonic images.
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